Don’t expect to see any of those e-mails between New Jersey Gov. Jon Corzine and his union boss ex-sweetie anytime soon – a court order notwithstanding.

State Attorney General Anne Milgram is vowing to appeal – on the taxpayers’ dime, of course – a judge’s ruling that Corzine must make public hundreds of pages of messages he shared with former squeeze Carla Katz, who heads the state’s largest government-workers union.

Superior Court Judge Paul Innes found that the messages – exchanged during labor contract talks – “created a clear potential for conflict” of interest on the governor’s part.

Corzine and Katz aren’t your typical ex-lovers, of course: Their relationship ended with a secretly negotiated multimillion-dollar settlement. Then it came out that the governor also enriched Katz’s brother-in-law – who’d lost his state job when he was caught digging through the tax records of Corzine’s political foes.

But Corzine insists that all this has nothing to do with keeping embarrassing (or, perhaps, incriminating?) information out of the public eye.

No, he says, this is a constitutional issue – and he’s only waging a protracted legal battle in order to protect future governors from having their private messages exposed.

That must be why Corzine’s lawyers spent hours trying to keep secret not just the e-mails themselves, but also the part of the judge’s ruling that revealed just how many messages are at issue.

State GOP chief Tom Wilson, who sued to get the e-mails, is putting Corzine to the test: He says he’ll drop the lawsuit (so that Innes’ ruling won’t create a legal precedent) if the governor voluntarily releases the messages.

So far, no response from Corzine. Anyone surprised?

As we’ve said from the outset: People with nothing to hide don’t spend so much time trying to hide it.